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Evgen [1.6K]
3 years ago
9

Find all the points on the curve y = 4x^4 − 8x^2 + 16x + 7 such that the tangent line to the curve is parallel to the line 16x −

y + 5 = 0.
Mathematics
1 answer:
IrinaVladis [17]3 years ago
4 0
Hello : 
the tangent has same slope of the line 16x -y +5 = 0  because parallel.
y = 16x + 5 
the slope is : 16
but : f'(x) = 16
f'(x) = 16x^3 - 16x +16
solve : 16x^3 - 16x +16 = 16
x^3 - x +1 =1
x^3 - x = 0
x(x² - 1 ) =0
x(x -1 )(x +1) =0
x=0 or x-1 =0 or x +1= 0
x=0 or x = 1 or x = -1
if : x = 0 : y = 4(0)^4 -8(0)^2+16(0) +7 =7
if : x =1 : y = 4(1)^4 -8(1)^2+16(1) +7 = 19
if : x = -1 : y = 4(-1)^4 -8(-1)^2+16(-1) +7 = -13
<span>the points : A(0,7)  , B(1 , 19) , c ( -1 , -13)</span>

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